Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+4y &= -7 \\ 5x-6y &= 7\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = -5x+7$ Divide both sides by $-6$ to isolate $y$ $y = {\dfrac{5}{6}x - \dfrac{7}{6}}$ Substitute this expression for $y$ in the first equation. $-4x+4({\dfrac{5}{6}x - \dfrac{7}{6}}) = -7$ $-4x + \dfrac{10}{3}x - \dfrac{14}{3} = -7$ Simplify by combining terms, then solve for $x$ $-\dfrac{2}{3}x - \dfrac{14}{3} = -7$ $-\dfrac{2}{3}x = -\dfrac{7}{3}$ $x = \dfrac{7}{2}$ Substitute $\dfrac{7}{2}$ for $x$ back into the top equation. $-4( \dfrac{7}{2})+4y = -7$ $-14+4y = -7$ $4y = 7$ $y = \dfrac{7}{4}$ The solution is $\enspace x = \dfrac{7}{2}, \enspace y = \dfrac{7}{4}$.